# Lecture3 - ECO ECO 220Y Lecture3 Describing Data by...

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ECO 220Y L t 3 ECO 220Y Lecture3 Describing Data by Graphical Technique P t 2 Part 2 Migiwa Tanaka Reading : 2.2,2.3,2.4 1

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O tli Outline Histogram – Interval Data Histogram Interval Data Shape of Histogram S l i & l ti Sample size & population Tabulation – Nominal/Ordinal Data 2
Hi t Histogram What can a histogram tell us? Overall distribution of observations. If they are clustering around a particular bin. If they are spread out. If there are more observations above average or below average. If it resembles known distribution, such as Normal distribution. Where should we pay particular attention when we inspect a histogram? Symmetry Positively/Negatively Skewed M d li Modality Bell-shaped, (Normal) 3

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S t Symmetry When a vertical line is drawn in the center of the shape and the right side and the left side of the shape is mirror image to each other the shape is said to be symmetric image to each other, the shape is said to be symmetric. 4
4 8 Perfect Symmetry .3 .4 sity .6 .8 sity .1 .2 Dens .2 .4 Dens 0 0 .5 1 1.5 2 2.5 x1 0 1 2 3 4 5 x2 .5 .25 2 .3 .4 ensity .15 .2. ensity 0 .1 .2 De 0 .05 .1 De 1 2 3 4 5 x3 2 4 6 8 10 x4 5

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Sk Skewness If the shape has long tail on the right but not on the left If the shape has long tail on the right, but not on the left, the shape is positively skewed .
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